# SDRS: Shape-Differentiable Robot Simulator

arXiv: https://arxiv.org/abs/2412.19127 · HTML: https://mlsanity.com/paper/2412.19127/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Dec 2024.

## Built on by (most cited first, 3 of 3)

- [Embodied Co-Design for Rapidly Evolving Agents: Taxonomy, Frontiers, and Challenges](https://mlsanity.com/paper/2512.04770/) (2025)
- [Simulation-Ready Cluttered Scene Estimation via Physics-aware Joint Shape and Pose Optimization](https://mlsanity.com/paper/2602.20150/) (2026)
- [On the Numerical Reliability of Differentiable Physics-Based Optimization for Robotic Material Manipulation](https://mlsanity.com/paper/2609.34666/) (2026)

## Abstract (arXiv)

Robot simulators are indispensable tools across many fields, and recent research has significantly improved their functionality by incorporating additional gradient information. However, existing differentiable robot simulators suffer from non-differentiable singularities, when robots undergo substantial shape changes. To address this, we present the Shape-Differentiable Robot Simulator (SDRS), designed to be differentiable under significant robot shape changes. The core innovation of SDRS lies in its representation of robot shapes using a set of convex polyhedrons. This approach allows us to generalize smooth, penalty-based contact mechanics for interactions between any pair of convex polyhedrons. Using the separating hyperplane theorem, SDRS introduces a separating plane for each pair of contacting convex polyhedrons. This separating plane functions as a zero-mass auxiliary entity, with its state determined by the principle of least action. This setup ensures global differentiability, even as robot shapes undergo significant geometric and topological changes. To demonstrate the practical value of SDRS, we provide examples of robot co-design scenarios, where both robot shapes and control movements are optimized simultaneously.